Question

a vector, b vector ,c vector are unit vectors and a + b + c = 0 . Find the value of 10(a-c).(a+b)​

Answer 1

1. Given a, b, c are unit vectors

2. Consider a as i unit vector in x - direction , b as j unit vector in y direction and c as k unit vector in z direction.

3. Also given that a+b+c = 0 that is a+b = -c

4. To find 10(a-c).(a+b)

5. Just write a+b as -c

6. Dot product of (a-c).c is a.c -c.c

7. As we know that in Dot product i.i = 1 and i.j and i.k = 0

8. So we get 0 - 1 = -1

9. So finally multiplying 10 with -1 we get - 10 as answer

10. So finally on solving 10(a-c).(a+b) we get - 10 as answer